I really agree with what Marda said.
I'll share a secret I don't often tell people outside my profession: when I was a nanny, it took almost a year for all of us (myself and the family) to become really "used to" each other. This includes me, a grown adult. A full year.
Your boyfriend's son sounds like he's had a LOT of transitions lately. A blended household (now he has two new people to get used to), potty training (which is, in my book, a big deal for some kids) and pretty typically, from my experience, you are going to see some regression in some area.
This is what I would do: love on him as much as you can. When he says he's awake, go in and read a story with him before he gets up. My son is 4.5 years old and even without all those huge transitions, he loves for me to snuggle him up in the mornings.
A. Maslow's "Heirarchy of Needs" (or what some call the child's "Staircase of Needs") identifies what children need in order to become self-actualizing people. First, their physical needs must be met. ("I have food, shelter, and someone to hold me.") Second, their need for security, proof that the world is a trustworthy place. I'll stop at the third (there are six): Belonging. "This is where I belong. This is my place." I think this little boy is stuck between second and third. He's asking for company and attention when he gets up, and gets nothing. It's up to you and your boyfriend to figure out how to help him feel that there is security in his new home, and part of that is responding to his needs, even if that means just helping him out of bed.
What you describe sounds sadly like a battle of wills. The adults want him to 'grow up'. He's in regression, which is really common for kids in this situation. Try to meet him halfway. This will take a long time. One book I recommend highly is "Taking Charge: Loving Discipline that Works at Home and School." by JoAnn Nordling. The area I would encourage you most to take to heart is regarding Positive Attention for Neutral Behaviors. (this is different from spending time with him or acknowledging his good behaviors, which you are doing.) He needs to know (not through words, but constant love and support) that he is loved for being just who he is. "Just who he is" right now is a little guy whose world just got turned upside down. No matter how his mother parents him, even if she's infantalizing him a bit, this book WILL help you be able to help him. I'd also suggest possibly family counseling, as I would suggest this when any two families become one.
Added: It's also really clear to see that you do care about this little boy and are trying to keep things stable as much as you can and as equal as you can with your daughter. Good for you. I have been where you are, by the way, in differing aspects of my work. It takes a lot of time for some kids to trust us, even if we think they're familiar with us. Having a lot of patience helps. I hope you let us know how things work out down the line.